What episode of GREY's anatomy do we meet Mark Sloan?

He initially appeared as a guest-star in the episode "Yesterday" of the second season, becoming a series regular from the third season episode "Sometimes a Fantasy", first broadcast in October 2006.

Why did Mark and Lexie die?

They still got that but there was a twist — Lexie was joined by Mark Sloan (Eric Dane). The on-again, off-again couple had gotten back together when they both died as a result of a plane crash in the Season 8 finale, and Seattle Grace Mercy West was subsequently renamed Grey Sloan Memorial Hospital in their memory.

Do Mark and Derek become friends again?

Derek subsequently left New York and later Addison followed suit, leaving Mark behind. He moved to Seattle to try to win them both back and in the end, he became good friends with both.